facility insurance?

watching a situation in our community unravel in a very unpleasant way, I am wondering what standard practice is in the US. We had a PE teacher try to catch the attention of a bus driver here as he was backing toward 4 children at a tournament. Things being what they are herein Cambodia, the teacher put his hand through the window and severed two arteries in his arm. It was horrific, but he was saved by some quick action. The ensuing hard feelings came about because his employer didn't want to assume responsibility in any way, shape or form.
If an instructor is hurt in the course of his duties does the gym just expect that person to have personal insurance or does the facility help? For example, I once saw a person gear up to stand up on a climbing segment of a class and the right pedal fell off. Pedal still stuck to the shoe, they slammed their right foot into the ground, while the speed of the wheel kept the other foot in motion. Shockingly sudden and unexpected. Fortunately that person wasn't hurt, but it was clearly a faulty (or unchecked) bike.
My question: if the instructor gets hurt while doing their job, what is the recourse?